Effect of scale adjustment on the comparison of item and ability parameters

Abstract

The standardized mean-squared difference (SMSD) has been used for summarizing the bias of parameter estimates in the three-parameter logistic (3PL) model. Due to the indeterminacy problem of the 3PL model, researchers must select a common scale for comparing the theoretical and estimated parameters. The use of different scales can yield noncomparable SMSD values, which in turn can affect the comparison of bias between different parameters. This research used three methods for selecting the common scale. Through a simulation,the three scaling methods were used to numerically demonstrate their effect on SMSD values. Index terms: equating, indeterminacy problem, Samejima scale, standardized mean-squared difference, Stocking and Lord scale, three-parameter logistic model.